CGAL 4.12.2 - 2D Triangulation
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The concept RegularTriangulationTraits_2
describes the requirements for the traits class of regular triangulations. It refines the concept TriangulationTraits_2
requiring the type CGAL::Weighted_point_2
and the power test predicate on those weighted points. A weighted point is basically a point augmented with a scalar weight. It can be seen as a circle when the weight is interpreted as a square radius. The power test on weighted points is the fundamental test to build regular triangulations as the side_of_oriented_circle
test is the fundamental test of Delaunay triangulations.
Kernel
.CGAL::Regular_triangulation_2
Types | |
typedef unspecified_type | Weighted_point_2 |
The weighted point type. More... | |
typedef unspecified_type | Power_side_of_oriented_power_circle_2 |
A predicate object, model of PowerSideOfOrientedPowerCircle_2 , that must provide operators for the power test applied to two, three, and four points. More... | |
typedef unspecified_type | Construct_point_2 |
A constructor type, model of Kernel::ConstructPoint_2 . More... | |
Optional Types | |
The following type/predicate is required for a call to | |
typedef unspecified_type | Compare_power_distance_2 |
A function object, model of Kernel::ComparePowerDistance_2 for comparing two power distances. More... | |
The following types/predicates are required to compute duals: | |
typedef unspecified_type | Construct_weighted_circumcenter_2 |
A function object, model of Kernel::ConstructWeightedCircumcenter_2 , that constructs the weighted circumcenter of three weighted points. More... | |
typedef unspecified_type | Construct_radical_axis_2 |
A function object, model of Kernel::ConstructRadicalAxis_2 , that constructs the radical axis of two weighted points. More... | |
Creation | |
RegularTriangulationTraits_2 () | |
Default constructor. | |
RegularTriangulationTraits_2 (const RegularTriangulationTraits_2 &) | |
Copy constructor. | |
RegularTriangulationTraits_2 & | operator= (const RegularTriangulationTraits_2 &) |
Assignment operator. | |
A function object, model of Kernel::ComparePowerDistance_2
for comparing two power distances.
Must provide the operator:
Comparison_result operator()(Point_2 p, Weighted_point_2 q, Weighted_point_2 r)
, which compares the power distance between p
and q
to the power distance between p
and r
.
A constructor type, model of Kernel::ConstructPoint_2
.
The operator()
extracts the bare point from a weighted point.
Point_2 operator() ( Weighted_point_2 p);
A function object, model of Kernel::ConstructRadicalAxis_2
, that constructs the radical axis of two weighted points.
Must provide the operator:
Line_2 operator() ( Weighted_point_2 p, Weighted_point_2 q);
A function object, model of Kernel::ConstructWeightedCircumcenter_2
, that constructs the weighted circumcenter of three weighted points.
Must provide the operator:
Point_2 operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r);
A predicate object, model of PowerSideOfOrientedPowerCircle_2
, that must provide operators for the power test applied to two, three, and four points.
Must provide the operators:
Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r, Weighted_point_2 s)
which is the power test for points p
, q
, r
and s
. p
, q
, r
are not collinear.Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r)
which is the degenerate power test for collinear points p
, q
, r
. p
, q
, r
are collinear and p != q
.Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q)
which is the degenerate power test for weighted points p
and q
whose corresponding bare-points are identical. p
and q
are identical. The weighted point type.
It has to be a model of the concept Kernel::WeightedPoint_2
.
Point_2
is requested by the concept TriangulationTraits_2
, which this concept refines.